Was math invented or discovered?

What is the basis for reason? And mathematics?

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Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

Hobbes' Choice wrote:Maths is just one of the human languages used to discuss and describe the world. Of the range so languages, it is low on ambiguity and low on nuance, and expression. It fails to address qualities, but is all about quantities.
Some find quantities qualitative:

Some find 7 inches more qualitative than 3; Some find 6 ft better than 4. 8)

Sure you can argue that the specific 'units' at issue are in themselves what defines quality. But I think this is just an illusion. A 'vector' for instance, is often defined as a scalar quantity, a linear unit, and some direction. "5 miles [north]", for instance might treat the "miles" and "north" as UNITS of quality, not quantity. But while they seem to be distinctly UNIQUE, these too can be interpreted quantitatively.

"5 miles [north]" may be reinterpreted as " 5 UNITS of an arbitrary agreed upon unit (not in itself 'real') in the arbitrary unit direction arbitrarily assigned of some 'origin' in common, like the North Star, that stays relatively constant."

The arbitrary realities which people agree to as 'units' are themselves determined based on other quantities and units as well. These are also done by the mere ways we observe and negotiate or confer about what we default to be 'real' of our powers of observation.

As such, we "discover" the reality. But the conventions we use to agree among each other to share these are the "invention" aspects and are about assigning those arbitrary 'units' we simply AGREE to conform to. This is what makes numbers appear invented only by perspective.
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Terrapin Station
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Re: Was math invented or discovered?

Post by Terrapin Station »

Both . . . kinda

It's a way of talking about our experience with/how we think about relations, in a highly abstract way. We don't literally "invent" how we think about relations in this abstract way--it's a factor of how our brains work, and it has to be consistent with how we experience the world, insofar as it makes sense to map it to empirical data. But it's not something we're discovering from outside of us.
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Re: Was math invented or discovered?

Post by akuma's chamber »

Terrapin Station wrote:Both . . . kinda

It's a way of talking about our experience with/how we think about relations, in a highly abstract way. We don't literally "invent" how we think about relations in this abstract way--it's a factor of how our brains work, and it has to be consistent with how we experience the world, insofar as it makes sense to map it to empirical data. But it's not something we're discovering from outside of us.
I'm not sure I understand. Isn't maths like logic in being a kind of language that we construct in order to make sense of things? So are you making a distinction between how we think about relations abstractly and how we construct models/languages to communicate and obtain some coherence about these abstract relations?
Philosophy Explorer
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Re: Was math invented or discovered?

Post by Philosophy Explorer »

akuma's chamber wrote:
Terrapin Station wrote:Both . . . kinda

It's a way of talking about our experience with/how we think about relations, in a highly abstract way. We don't literally "invent" how we think about relations in this abstract way--it's a factor of how our brains work, and it has to be consistent with how we experience the world, insofar as it makes sense to map it to empirical data. But it's not something we're discovering from outside of us.
I'm not sure I understand. Isn't maths like logic in being a kind of language that we construct in order to make sense of things? So are you making a distinction between how we think about relations abstractly and how we construct models/languages to communicate and obtain some coherence about these abstract relations?
Logic is one of math's many branches (and a very important one).

PhilX
Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

Philosophy Explorer wrote:
akuma's chamber wrote:
Terrapin Station wrote:Both . . . kinda

It's a way of talking about our experience with/how we think about relations, in a highly abstract way. We don't literally "invent" how we think about relations in this abstract way--it's a factor of how our brains work, and it has to be consistent with how we experience the world, insofar as it makes sense to map it to empirical data. But it's not something we're discovering from outside of us.
I'm not sure I understand. Isn't maths like logic in being a kind of language that we construct in order to make sense of things? So are you making a distinction between how we think about relations abstractly and how we construct models/languages to communicate and obtain some coherence about these abstract relations?
Logic is one of math's many branches (and a very important one).

PhilX
I rather compare it to verbs and nouns within sentences. So Logic is a math and math is a logic in the same way we can treat nouns as verbs and verbs as nouns using relative forms of the particular words in context to the structure of the sentence that combines them together.

Noun + (Verb + Noun) = Sentence.
(Verb + Noun) = Predicate or new form structure.
Sentence = New Noun form.

The 'forms' are the logic which include Math. Math is just the Sentences using the DOMAIN of Numbers as Nouns, and the DOMAIN of verbs to be the 'logical connectives' or action OPERATORS between those nouns (as numbers) that make new 'sense' (Sentences). These then act as New Nouns that can be replaced back into another Sentence as Nouns.

The 'verbs' in Math are derived by merely associating the nouns as numbers. For instance, beginning with any two numbers (nouns) where one is 'subject' to the other as 'object', is related:

5 Relates to 3 in some way

Then math operators are determined by defining some relation between these, like 5 is (2 more than) 3. Taking many such relations of Specific numbers (nouns) creates a pattern that DEFINES unique relationships:

5 is to 3 by the relation (subject - 2).
7 is to 5 by the relation (subject - 2).

The pattern here might be inferred that some concept '2' exists and by the verb, "-". These thus define both the logic of Math, where math is the limiting relation using numbers as nouns and operators/relations as verbs.

The same can be done WITH the Grammar too. So logic is the General form of Specific logics, like math or grammar or computer languages, etc.
But math too can be a basic logic with respect to some finer logic, which makes THAT system a "logic BASED on Math", like Calculus.

Math, thus is under Logic, though both ARE Logic.
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Hobbes' Choice
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Re: Was math invented or discovered?

Post by Hobbes' Choice »

Scott Mayers wrote:
Hobbes' Choice wrote:Maths is just one of the human languages used to discuss and describe the world. Of the range so languages, it is low on ambiguity and low on nuance, and expression. It fails to address qualities, but is all about quantities.
Some find quantities qualitative:

Some find 7 inches more qualitative than 3; Some find 6 ft better than 4. 8)

I consider this to make no sense what ever.


Sure you can argue that the specific 'units' at issue are in themselves what defines quality. But I think this is just an illusion. A 'vector' for instance, is often defined as a scalar quantity, a linear unit, and some direction. "5 miles [north]", for instance might treat the "miles" and "north" as UNITS of quality, not quantity. But while they seem to be distinctly UNIQUE, these too can be interpreted quantitatively.

"5 miles [north]" may be reinterpreted as " 5 UNITS of an arbitrary agreed upon unit (not in itself 'real') in the arbitrary unit direction arbitrarily assigned of some 'origin' in common, like the North Star, that stays relatively constant."

The arbitrary realities which people agree to as 'units' are themselves determined based on other quantities and units as well. These are also done by the mere ways we observe and negotiate or confer about what we default to be 'real' of our powers of observation.

As such, we "discover" the reality. But the conventions we use to agree among each other to share these are the "invention" aspects and are about assigning those arbitrary 'units' we simply AGREE to conform to. This is what makes numbers appear invented only by perspective.
There is no such thing as 5 in nature. One five mile length along a road is not the same as any other. Nature has no integers. Take an orange, and another one. The phrase two oranges is a human conceived convenience, as not two oranges are the same, do not occupy the same space and time, can not weight the same, do not have the same number of molecules as each other, or even the same number each of them had 3 seconds ago, 1 orange is NOT EQUAL to 1 orange.
There are no straight lines in nature. Circles are incommensurable to number systems and are never resolved due to PI. There are many irrational numbers. point are arbitrary, and relative to a range of motions, and gravitic/time distortions.
Circles and other 2D shapes cannot exist, except in the imagination.


In short the universe is not written in maths.
surreptitious57
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Re: Was math invented or discovered?

Post by surreptitious57 »

Hobbes Choice wrote:
In short the universe is not written in maths
The laws of physics are formulated in mathematical language but the
universe is not maths. For the map and the terrain are not the same
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Re: Was math invented or discovered?

Post by Terrapin Station »

akuma's chamber wrote:I'm not sure I understand. Isn't maths like logic in being a kind of language that we construct in order to make sense of things?
That's basically what I'm saying above.

So are you making a distinction between how we think about relations abstractly and how we construct models/languages to communicate and obtain some coherence about these abstract relations?
Not really, no. I mean I wouldn't say they're identical, in that expressions are not identical to thoughts, but I wasn't focusing on that above.
Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

Hobbes' Choice wrote:
Scott Mayers wrote:
Hobbes' Choice wrote:Maths is just one of the human languages used to discuss and describe the world. Of the range so languages, it is low on ambiguity and low on nuance, and expression. It fails to address qualities, but is all about quantities.
Some find quantities qualitative:

Some find 7 inches more qualitative than 3; Some find 6 ft better than 4. 8)

I consider this to make no sense what ever.


Sure you can argue that the specific 'units' at issue are in themselves what defines quality. But I think this is just an illusion. A 'vector' for instance, is often defined as a scalar quantity, a linear unit, and some direction. "5 miles [north]", for instance might treat the "miles" and "north" as UNITS of quality, not quantity. But while they seem to be distinctly UNIQUE, these too can be interpreted quantitatively.

"5 miles [north]" may be reinterpreted as " 5 UNITS of an arbitrary agreed upon unit (not in itself 'real') in the arbitrary unit direction arbitrarily assigned of some 'origin' in common, like the North Star, that stays relatively constant."

The arbitrary realities which people agree to as 'units' are themselves determined based on other quantities and units as well. These are also done by the mere ways we observe and negotiate or confer about what we default to be 'real' of our powers of observation.

As such, we "discover" the reality. But the conventions we use to agree among each other to share these are the "invention" aspects and are about assigning those arbitrary 'units' we simply AGREE to conform to. This is what makes numbers appear invented only by perspective.
There is no such thing as 5 in nature. One five mile length along a road is not the same as any other. Nature has no integers. Take an orange, and another one. The phrase two oranges is a human conceived convenience, as not two oranges are the same, do not occupy the same space and time, can not weight the same, do not have the same number of molecules as each other, or even the same number each of them had 3 seconds ago, 1 orange is NOT EQUAL to 1 orange.
There are no straight lines in nature. Circles are incommensurable to number systems and are never resolved due to PI. There are many irrational numbers. point are arbitrary, and relative to a range of motions, and gravitic/time distortions.
Circles and other 2D shapes cannot exist, except in the imagination.


In short the universe is not written in maths.
Then how do we even determine ANYTHING as 'real' through generalizing?

XXXXX
&&&&&
.....
(37)(37)(37)(37)(37)

'Scientifically' we might take the above PATTERNS from observation to try to infer some generalization or "law". If you cannot infer the concept of the above generalizations to MEAN the concept we simplify through the label, "5", or to the word label, "five", I'm not sure how you can treat ANYTHING we observe as anything beyond the specific unique things themselves. That is, the word, "five" should have no meaning if you can't even associate it to something 'real', let alone those distinct things above. How do you know that you 'see' any "X"s on the first line? Do you deny that the marks are real or just to the specific interpretation of 'X' to mean something arbitrarily tossed out there as something unique each time. How do you know that if you saw anything once, that any repeated instance occurs afterward because the 'memory' that allows you to recall such a thing in the past is no more 'real' than what you are asserting about the conceptual meaning of "five"?

Numbers ARE as real as anything AND they have way more validity than anything else that we know because they are more universally understood than to anything specific you uniquely observe. You could NOT possibly associate anything in memory if you don't have a function to assign WHAT you see with number, as its most basic common meaning.

I can say, the following symbol,

D

is a letter that stands for the unique (note uni- means ONE and -que, WHAT-ness or KIND) semantically referring to something at least one thing. If you don't think this has the property of being ONE, then it is NOT unique. If you deny this, still, take any box, and place quantity of oranges in it. Does that quantity remain 'true' or can you not be able to determine through your senses whether there is only one, two, five, or any other IMAGINARY concept for it?

The "arbitrary" LABEL we assign is the UNREAL portion of it. But this is just the property of "zeroness", just as a point is that which has NO space. That "D" above doesn't HAVE to be the fourth letter of the alphabet nor to the thing we DENOTE by the sound we make when speaking. But if you treat the symbol as a model not to be real in itself, there is NO POSSIBLE way you could remember anything at any moment because you could not IDENTIFY (the concept of placing the PROPERTY AND EXISTENCE OF ONE TO THE RULE: X = X is 'true) If this wasn't true, you'd see X = y = 4 = span = "for my Bonny lies over the ocean", etc. The lunacy I'm showing is that you cannot find even what anything is (any- ONE-LIKE + -thing) if you cannot accept numbers (their meaning, not the symbols we model them on), as real.
Last edited by Scott Mayers on Thu Oct 20, 2016 5:33 pm, edited 1 time in total.
Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

surreptitious57 wrote:
Hobbes Choice wrote:
In short the universe is not written in maths
The laws of physics are formulated in mathematical language but the
universe is not maths. For the map and the terrain are not the same
See my above response. This is an infinite regress though, just as when you assign some "god" as an origin that begs where it comes from. The 'source' is understood to be REAL but unable to appropriately LABELED because the LABELS are NOT the literal thing. But you CAN infer that something meaningful is 'true'. "God" is only a faulty argument because it specifically identifies a human biased interpretation of what it MEANS. But if you LABEL the concept of an 'origin' in meaning generically without placing emphasis to the symbol, the reality modeled by the symbol is itself something real.

The LAWS of Physics are LOGICAL LAWS we infer by patterns. If you assume you cannot infer numbers, nor can you assume laws of physics, let alone any thing OF it. So you'd have to admit that even Physics would have to be unreal or "arbitrary" symbolized models that are not real.

Its circular and unable to be reconciled. Anything you sense, you cannot interpret as 'real' because your senses are secondary interpretations of what the objects out there are. What is 'red ball 2 feet in front of me' is just as symbolic to the literal experience and you'd have to avoid even describing reality other than to HOW you USE the symbols.

[This is what Heisenberg's Uncertainty principle derived from by the way. He asserted that since Observations themselves bias the interpretation of what we are observing regardless, we can't actually be certain that what we seem to observe is any more certain because the act of observing lies in between us and nature outside of us, how can you be certain that HOW you observe is NOT what is biasing WHAT we determine as 'real'?]
Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

[s]Terrapin[/s] Hobbe's, I just saw the blue note you added to not knowing what I meant. Ask some heterosexual girl (or homosexual guy) which she'd prefer and whether it might have meaning or not. I thought the smile might have hinted at both the humor and the point about how quantity can have a significant qualitative meaning.
Last edited by Scott Mayers on Thu Oct 20, 2016 6:45 pm, edited 1 time in total.
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Re: Was math invented or discovered?

Post by Terrapin Station »

Scott Mayers wrote:Terrapin, I just saw the blue note you added to not knowing what I meant. Ask some heterosexual girl (or homosexual guy) which she'd prefer and whether it might have meaning or not. I thought the smile might have hinted at both the humor and the point about how quantity can have a significant qualitative meaning.
I'm lost re what you're referring to here. ?
Scott Mayers
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Re: Was math invented or discovered?

Post by Scott Mayers »

Terrapin Station wrote:
Scott Mayers wrote:Terrapin, I just saw the blue note you added to not knowing what I meant. Ask some heterosexual girl (or homosexual guy) which she'd prefer and whether it might have meaning or not. I thought the smile might have hinted at both the humor and the point about how quantity can have a significant qualitative meaning.
I'm lost re what you're referring to here. ?
Oops, it looks like it was Hobbe's, not you. See the reference above where he last responded to me.
surreptitious57
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Re: Was math invented or discovered?

Post by surreptitious57 »

Scott Mayers wrote:
This is what Heisenbergs Uncertainty principle derived from by the way. He asserted that since observations them selves bias the interpretation
of what we are observing regardless we cant actually be certain that what we seem to observe is any more certain because the act of observing
lies in between us and nature outside of us how can you be certain that HOW you observe is NOT what is biasing WHAT we determine as real?
Inter subjectivity removes the potential bias of single person perspectives
When everyone is experiencing the same reality it is less likely to be false
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Re: Was math invented or discovered?

Post by Hobbes' Choice »

Scott Mayers wrote:
Hobbes' Choice wrote:
Scott Mayers wrote: Some find quantities qualitative:

Some find 7 inches more qualitative than 3; Some find 6 ft better than 4. 8)

I consider this to make no sense what ever.


Sure you can argue that the specific 'units' at issue are in themselves what defines quality. But I think this is just an illusion. A 'vector' for instance, is often defined as a scalar quantity, a linear unit, and some direction. "5 miles [north]", for instance might treat the "miles" and "north" as UNITS of quality, not quantity. But while they seem to be distinctly UNIQUE, these too can be interpreted quantitatively.

"5 miles [north]" may be reinterpreted as " 5 UNITS of an arbitrary agreed upon unit (not in itself 'real') in the arbitrary unit direction arbitrarily assigned of some 'origin' in common, like the North Star, that stays relatively constant."

The arbitrary realities which people agree to as 'units' are themselves determined based on other quantities and units as well. These are also done by the mere ways we observe and negotiate or confer about what we default to be 'real' of our powers of observation.

As such, we "discover" the reality. But the conventions we use to agree among each other to share these are the "invention" aspects and are about assigning those arbitrary 'units' we simply AGREE to conform to. This is what makes numbers appear invented only by perspective.
There is no such thing as 5 in nature. One five mile length along a road is not the same as any other. Nature has no integers. Take an orange, and another one. The phrase two oranges is a human conceived convenience, as not two oranges are the same, do not occupy the same space and time, can not weight the same, do not have the same number of molecules as each other, or even the same number each of them had 3 seconds ago, 1 orange is NOT EQUAL to 1 orange.
There are no straight lines in nature. Circles are incommensurable to number systems and are never resolved due to PI. There are many irrational numbers. point are arbitrary, and relative to a range of motions, and gravitic/time distortions.
Circles and other 2D shapes cannot exist, except in the imagination.


In short the universe is not written in maths.
Then how do we even determine ANYTHING as 'real' through generalizing?

We generalise to make a generalisation. what has this got to do with determining reality.
Animals know what is real, they do not need any Maths.



XXXXX
&&&&&
.....
(37)(37)(37)(37)(37)

'Scientifically' we might take the above PATTERNS from observation to try to infer some generalization or "law". If you cannot infer the concept of the above generalizations to MEAN the concept we simplify through the label, "5", or to the word label, "five", I'm not sure how you can treat ANYTHING we observe as anything beyond the specific unique things themselves. That is, the word, "five" should have no meaning if you can't even associate it to something 'real', let alone those distinct things above. How do you know that you 'see' any "X"s on the first line? Do you deny that the marks are real or just to the specific interpretation of 'X' to mean something arbitrarily tossed out there as something unique each time. How do you know that if you saw anything once, that any repeated instance occurs afterward because the 'memory' that allows you to recall such a thing in the past is no more 'real' than what you are asserting about the conceptual meaning of "five"?

Numbers ARE as real as anything AND they have way more validity than anything else that we know because they are more universally understood than to anything specific you uniquely observe. You could NOT possibly associate anything in memory if you don't have a function to assign WHAT you see with number, as its most basic common meaning.

I can say, the following symbol,

D

is a letter that stands for the unique (note uni- means ONE and -que, WHAT-ness or KIND) semantically referring to something at least one thing. If you don't think this has the property of being ONE, then it is NOT unique. If you deny this, still, take any box, and place quantity of oranges in it. Does that quantity remain 'true' or can you not be able to determine through your senses whether there is only one, two, five, or any other IMAGINARY concept for it?

The "arbitrary" LABEL we assign is the UNREAL portion of it. But this is just the property of "zeroness", just as a point is that which has NO space. That "D" above doesn't HAVE to be the fourth letter of the alphabet nor to the thing we DENOTE by the sound we make when speaking. But if you treat the symbol as a model not to be real in itself, there is NO POSSIBLE way you could remember anything at any moment because you could not IDENTIFY (the concept of placing the PROPERTY AND EXISTENCE OF ONE TO THE RULE: X = X is 'true) If this wasn't true, you'd see X = y = 4 = span = "for my Bonny lies over the ocean", etc. The lunacy I'm showing is that you cannot find even what anything is (any- ONE-LIKE + -thing) if you cannot accept numbers (their meaning, not the symbols we model them on), as real.

Not sure what the problem here is.
We all of us had a rich experience of the world before we learned any maths, and we live most of our lives without daily reference to it.

Numbers are conceptual. Cups and apples exist without them. Does a cup need to know how many other cups in the cupboard before it can exist?

If no one had ever invented maths to count ONE world, would the world still have existed? Maths is a descriptive language.


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